How do I split the mesh using another plane?
Boolean didn't work because you have inner faces that make it fail. That said you can limit the Wave modifier to the group you want, to do so create a group in Weight Paint mode (once done you can soften the weight with the Blur brush) or in the Properties panel &gt; Object Data &gt; Vertex Groups &gt; Assign. Then choose this group in the Wave modifier (and also in the Displace modifier if you've used one). Here only the top vertices have been assigned to the group (except the small part that you didn't want) so the bottom won't be affected: